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### Open Access Journals

DCDS

For Axiom A diffeomorphisms and equilibrium states, we prove a Large deviations result for the sequence of successive return times into a fixed Borel set, under some assumption on the boundary.
Our result relies on and extends the work by Chazottes and Leplaideur who considered cylinder sets of a Markov partition.

ERA-MS

We present a method to construct equilibrium states via inducing. This method can be used for some non-uniformly hyperbolic dynamical systems and for non-Hölder continuous potentials. It allows us to prove the existence of phase transition.

keywords:

DCDS

We study the time of $n$th return of orbits to some given
(union of) rectangle(s) of a Markov partition for an Axiom A
diffeomorphism. Namely, we prove the existence of a scaled
generating function for these returns with respect to any Gibbs
measure. As a by-product, we derive precise large deviation
estimates and a central limit theorem for these return times. We
emphasize that we look at the limiting behavior in term of number
of visits (the size of the visited set is kept fixed). Our
approach relies on the spectral properties of a one-parameter
family of induced transfer operators on unstable leaves crossing
the visited set.

keywords:
large deviations
,
Successive return times
,
Axiom A
,
central limit theorem.
,
transfer operator

## Year of publication

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